Wrong, David did repent..
15And Nathan departed unto his house. And YAHWEH struck the child that Uriah's wife bare unto David, and it was very sick. 16David therefore besought God for the child; and David fasted, and went in, and lay all night upon the earth. 17And the elders of his house arose, and went to him, to raise him up from the earth: but he would not, neither did he eat bread with them.
18And it came to pass on the seventh day, that the child died. And the servants of David feared to tell him that the child was dead: for they said, Behold, while the child was yet alive, we spake unto him, and he would not hearken unto our voice: how will he then vex himself, if we tell him that the child is dead?
19But when David saw that his servants whispered, David perceived that the child was dead: therefore David said unto his servants, Is the child dead? And they said, He is dead.
20Then David arose from the earth, and washed, and anointed himself, and changed his apparel, and came into the house of YAHWEH, and worshipped: then he came to his own house; and when he required, they set bread before him, and he did eat.